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MSC/CONSTRUCT - Topology and Shape

Optimization of Large Real World Structures using

the distributed parallel MSC/NASTRAN

Contents

1 Introduction

2 Applied Software

2.1 MSC/CONSTRUCT SHAPE Optimization

2.2 MSC/CONSTRUCT TOPOLOGY Optimization2.3 Parallel MSC/NASTRAN (PMN) Solver Technology

2.4 HIPOP Sofware

3 The Benchmarking Machine

3.1 Node Types

3.2 File Systems

4 Topology Optimization with MSC/CONSTRUCT and PMN

5 CoupledShapeOptimizationwithMSC/CONSTRUCTandSOL200

6 Conclusion

7 Acknowledgements

8 References

8.1 Shape Optimization

8.2 Topology Optimization

Author:Dipl.-Ing. O. MllerFE-DESIGN GmbHHaid-und-Neu-Strasse 776131 Karlsruhe/GermanyPhone +49-721-96467-12Fax +49-721-96467-29Email: [email protected]


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1. Introduction

In the tough international competition, companies can only survive if, besides highly in-novative power, they can provide strongly cost optimized products. Therefore in newprocedures like the Simultaneous Engineering the calculation engineer is already inte-

grated in the concept phase of the product development process. Efficient methods ofworking require powerful optimization algorithms to be provided in addition to the dis-crete methods (FEM/BEM) that proved worth while to support the calculation engineerin the draft and design phase (see Figure 1). Almost all FEM codes have integrated si-zing optimization capabilities to support the calculation engineer.

In this context new optimization criteria and control strategies for sizing, shape and to-pology optimization were found at the Institute of Machine Design of the University ofKarlsruhe, Germany, in 1991. Based on these new strategies the computer programCAOSS (Computer Aided Optimization System Sauter) was developed at the institutein cooperation with FE-DESIGN, Karlsruhe, Germany. In 1994 the program was awar-ded the European Academic Software Award by the European Commission, DG XIII,to be the best program in the field of mechanics. This formed the basis for the productwhich is now known as MSC/CONSTRUCT with its options TOPOLOGY and SHAPEand is licensed to MSC on a worldwide basis since 1997. An important step forwardwas the integration of MSC/CONSTRUCT within the MSC/PATRAN environment.

For both sizing and shape optimization a first design proposal, which is used as thestart design, must exist. The objective of general structural optimization methods, such

Figure 1: Topology and Shape Optimization in the Product Development Process


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as topology optimization, is to provide even this first design proposal. The designercreates only the design space which includes the future component. Subsequently thefunctionally required boundary conditions are applied. The efforts for the modeling andpreparation are extremely low. The optimum structural shape with the appropriate to-pology is calculated utilizing a FEM program and issued as a design proposal which

might be refined by the designer.

Compared with the sizing and shape optimization the numerical efforts of this iterativeprocess strongly increase. Therefore currently only components with 15.000 to a ma-ximum of 30.000 elements could be calculated, even when using powerful worksta-tions. Due to the high number of iterations (typically between 20 to 30 iterations) andthe fact that approx. 90 to 95% of the CPU time is used by the FEM program for theanalysis, the performance and the resource requirements of the FEM program are ofparticular importance.

For the last two years certain FEM solvers (like MSC/NASTRAN) were ported to hard-

ware platforms with distributed memory. Using those, a considerable reduction of theprice/performance ratio combined with impressive speedups was shown for the parallelcode. This facts make the utilization of these codes interesting to industrial users. Wi-thin the HIPOP (HIgh Performance OPtimization) project the coupling of the distributedparallel MSC/NASTRAN (PMN) and MSC/CONSTRUCT was realized.

The benchmarking of real world applications from companies like BMW, PININFARI-NA, AUSTRIAN AEROSPACE and FE-DESIGN showed the reliability and efficiency ofthe approach. Even for models far beyond 200.000 degrees of freedom and with anumber of load cases speedups of 3 to 4 were achieved on 8 processors.


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2. Applied Software

2.1 MSC/CONSTRUCT SHAPE Optimization

Using shape optimization methods with a parametric approach as implemented in the

most FEM programs the number of design variables must not be too large. This causesthe numerical efforts to increase drastically due to the nonlinear increase of the calcu-lation of the sensitivities. Therefore with these approaches, models with more than 200design variables begin to incurr significant numerical overhead. The control algorithmswith mechanical knowledge, which are implemented in the shape optimization programMSC/CONSTRUCT SHAPE for linear statics, are independent of the number of designvariables ([3],[4],[5]). Therefore they allow a high number of design variables.

Thus real world models can be handled in industrial applications. Also the high numberof design variables is advantageous for the higher flexibility of the solution, e.g. thecreation of optimal structures which would not be possible with a restricted parametric

approach.

The pictures show a 10.000 element 3D model of a primary flywheel clutch (see Fig-

ure 2). The evolution from a cylindrical geometry of the bores to a more complex

geometry which fits optimal to the loads and boundary constraints is obvious. This

solution would be gained using a parametric approach only with extreme efforts.

To meet productional and functional requirements appropriate functionalities were im-plemented in MSC/CONSTRUCT SHAPE.

Figure 2: Shape Optimization of a Flywheel


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A further benefit of MSC/CONSTRUCT is, that its preprocessing and postprocessing isfully included in MSC/PATRAN. Therefore the model setup capabilities provided fromMSC/PATRAN can directly be utilized for the definition of the optimization model. Thelook-and-feel of the user interface is in MSC/PATRAN design which on the one sidemaintains the user in its known environment and on the other side guarantees astraightforward introduction to the optimization with MSC/CONSTRUCT.

Figure 3: Postprocessing of a Shape Optimized Connecting Rod


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2.2 MSC/CONSTRUCT TOPOLOGY Optimization

Topology optimization is the latest type of optimization for the area of mechanicallyloaded components. With topology optimization structural parts are identified which donot contribute to the components behaviour. In other words: In a given design space

material is distributed in such a way that under certain constraints specific objectivesare met.

Currently there are three main fields where topology optimization is applied: The very early design phase, where the design can easily be changed. Here the

topology optimization starts from a rough design proposal. When potential for reducing the components stresses and weight needs to be

identified. Here the topology optimization starts from an already existing designmodel.

When parts of an already existing structure are completely redesigned .

As for the shape optimization MSC/CONSTRUCT TOPOLOGY also uses for the topo-logy optimization a mechanical approach ([8],[9],[10]).

Compared with the shape optimization the main difficulty in topology optimization is theextremely high number of design variables in connection with the high number of requi-red FEM calculations (approx. 20 to 30). As seen in Figure 4 the solution depends onthe resolution of the initial structure. Therefore even on high performance workstationsthe model size was restricted to 20.000 to maximum 30.000 elements before HIPOP.Through the implementation of an approach with mechanical knowledge in MSC/CON-STRUCT TOPOLOGY the CPU time requirement of the topology optimization moduleis only 5 to 10%.

Figure 4: Topology Optimization of a Solid Rocker Arm


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2.3 Parallel MSC/NASTRAN (PMN) Solver Technology

In the ESPRIT III project Europort-1, Porting Work Area Parallel MSC/NASTRAN(PMN), MSC started to port MSC/NASTRAN to distributed parallel hardware architec-tures. The distributed parallel modules developed in this project are available since

September 1997 in the commercial MSC/NASTRAN release V69.2.

On serial computers and for large problems, the numerical solution modules typicallyrequire 85% to 95% of the total elapsed time. Therefore, parallelizing just these modu-les on their own gives a significant increase of performance. This strategy is well suitedto giving a good return from moderately parallel systems. By taking this approach, it ispossible to gain benefits from parallelization without the need for extensive modificationto the code structure.

In the frame of this project a considerable reduction of the price/performance ratio wasshown for the parallel code, which makes the utilization of PMN interesting to industrialusers.

The speedups shown in Figure 5 are measured only for the solution module itself anddo not contain the computing times required for the element stiffness matrix generationas well as for the data recovery.

Figure 5: Benchmark from EUROPORT1 (Courtesy of BMW AG and MSC)


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2.4 HIPOP Sofware

Besides aspects of streamlining the optimization process through adaption techniques,the major task within the HIPOP project was to replace the serial MSC/NASTRAN withthe parallel MSC/NASTRAN (PMN).

Figure 6: Flow chart of MSC/CONSTRUCT and Parallel MSC/NASTRAN (PMN)


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3. The Benchmarking Machine

The benchmarks were executed on an IBM-SP2, located at the Scientific Supercom-puting Center (SSC) of the University of Karlsruhe, Germany. This is the currently mostpowerful IBM parallel computer in Europe. The machine comprises 256 nodes with a

total peak performance of 107 Giga Flops, 130 Giga Byte Main Memory and 2.1 TeraByte disk space.

3.1 Node Types

The machine runs three types of processors: 16 thin2 nodes with 67 MHz Power2 processors:

These nodes with each 128 MB main memory are used for serving the parallelfile system (PIOFS). Each server is connected to 8 disks with 2GB each mean-

ing that a total of 256 GB PIOFS workspace is provided. For safety reasons thedata in the PIOFS is currently mirrored, which results in a net capacity of only128 GB.

160 thin P2SC nodes with 120 MHz P2SC processors:These nodes are used for the parallel production jobs. Each node has 512 MBmain memory.

80 wide2 nodes with 77 MHz Power2 processors:These nodes have 256 MB, 512 MB or 2 GB main memory. They are used fordifferent applications like server and compute node for serial and parallel batchjobs and for interactive use.

The machine is partitioned into several pools for different requirements. For our bench-marks two homogeneous node pools were available, the so-called production pool

Figure 7: Scientific Supercomputing Center (SSC) Karlsruhe


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and the general pool (FE pool). The production pool consists of 160 P2SC nodes,each of which is equipped with 512 MB local main memory and 2 GB local wide SCSI-2 disks. The FE pool contains 8 wide2 nodes with 2 GB local main memory and 8 GBlocal SSA disks each. Parallel jobs using a heterogeneous node pool are currently notsupported on the machine in Karlsruhe. The theoretical peak bandwidth of the commu-

nication network in this machine is approximately 150 MB per second.

3.2 3.2File Systems

The machine runs totally under the control of DCE/DFS (Distributed Computing Envi-ronment/Distributed File Systems). This makes the file handling very user friendly asthe user has not to take care on which specific disk his data are stored.

Data Management during the Optimization Process

Besides aspects of fast CPUs and large main memory, the I/O and therefore the data

flow management is very important for FEM applications. Figure 8 shows the data flowrealized with the newly developed control programs for the use of the general and theproduction class nodes.

The application programs and the model data are located on the DFS-Servers in theUser home File System ($HOME). When the user starts the optimization the controlprogram copies the model data to the working directory ($WORK). During the optimi-zation the model data is stored in this file system ($WORK is a Parallel Input OutputFile System) whereas the temporary data (scratch files) is written to the local disksusing the $TEMP_LOCAL environment variable.

This ensures maximum I/O rates while having a large file system for the data accumu-

Figure 8: User File Systems within SP


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lated during the optimization at the same time. During the optimization process of thisextremely large structures 20 to 40 GB temporary disk space is easily needed.

4. Topology Optimization with MSC/CONSTRUCT and PMN

The target of the BMW benchmark was to evaluate the use of current topology optimi-zation in the design of extremely large and complex structures. To show this the shellstructure of a BMW 3-series car was selected.

In this approach the sheet metal from the wheel housing was completely removed andreplaced by solid elements. The topology optimization software should then find themaximum stiffness for a given amount of material which satisfies all 6 load cases. Thefour different boundary conditions simulate various driving situations, for instance cor-nering.

To get an adequate resolution for the resulting structure an extremely fine mesh is re-

quired. For testing and evaluation purposes firstly the wheel housing was filled with arelatively coarse tetrahedral mesh. This resulted in a model containing 20,718 nodesand 14,821 elements, the shell elements of the remaining structure already counted.

To achieve the required resolution and to simplify the setup of the topology optimizationmodel a second structure was created using the voxel technology. The voxel techno-logy has its origin in the CAD/CAE-world where it is used e.g. to simulate enginemaintenance processes. For our purposes it allows a very simple representation of thewheel housing and furthermore voxels are extremely easy to generate.

Like 2-dimensional pictures are printed with simple pixels, any CAD model can be de-scribed with the 3-d pendant of the pixels: the voxels. A voxel is simply a small cubewith a certain edge length. The smaller the edge length the higher the resolution of themodel. The data volume is reduced dramatically (often the reduction to 1 per cent ofthe original data volume is possible) by transforming the description of volumes, planesand points of the original CAD model to a common voxel model.

Figure 9: BMW Series-3 Benchmarking Model


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The difficulty with voxel-based FE models is that one comes easily to extremely largestructures and therefore require high resources. The voxel model generated for the HI-POP project contains 91,162 nodes and 81,254 elements resulting in 287,965 degreesof freedom. This model needs to be solved for the above mentioned 6 load cases with4 different boundary sets.

In Figure 10 the resulting elapsed computing times (left axis) and the correspondingspeedups (right axis) versus the number of processors are shown.

The data recovery operations were not part of the parallelization and do not scale with

the number of processors. This can clearly be seen from the diagram when looking atthe elapsed times of the optimization loop. The curve of the times for one optimizationloop with the HIPOP improvements is parallel to the one with the initial software (1 Opt.-Loop (old)).

From the diagram one can learn that the elapsed time required for one optimizationloop was reduced from 79,000 sec. to 25,000 on 8 processors. That means that theimprovements lead to a speedup factor of 3.17.

Figure 10: Benchmark BMW Fine Voxel Model


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5. Coupled Shape Optimization with MSC/CONSTRUCT andSOL200

An optimization model is required for an optimization in the same way as an analysismodel is required for a finite element analysis. For shape optimization it also covers the

statement of allowable shape changes. In the MSC/NASTRAN SOL200 these shapechanges are expressed by socalled shape basis vectors ([7] Moore, G.J.: MSC/NA-STRAN Design Sensitivity and Optimization, Users Guide, Version 68, 1994). The nu-merical optimization algorithm than determines the best linear combination of theseshape basis vectors.

To set up a SOL200 optimization model one major task is to derive shape basis vec-tors, which have sufficient influence on the optimization objective and constraints ([1]Raasch, I.; Irrgang, A.: Shape Optimization with MSC/NASTRAN; MSC/NASTRAN Eu-ropean Users' Conference, Rome, 1988,[2] Chargin, M.; Raasch, I.: Structural Optimi-zation with MSC/NASTRAN revisited [3]in Version 66, MSC/NASTRAN EuropeanUser's Conference, Paris, 1990,[6] Raasch, I.: Structural Optimization with Solution2001 in the Design Process; MSC/NASTRAN World Users' Conference, Lake BuenaVista, 1994). Because the creation and definition of the shape basis vectors must bemade manually, it is time consuming and costly especially for 3D structures.

Other optimization approaches are the optimality criteria procedures like the ones im-plemented in MSC/CONSTRUCT SHAPE. They often have the advantage to generatethe new shape without the necessity of shape vectors. Their disadvantage is their lackof handling arbitrary object functions and constraints. Therefore the idea within HIPOPwas to use an optimality criteria for the generation of shape basis vectors and to use

the mathematical optimization approach of the SOL200 to fulfill arbitrary objectives andconstraint functions.


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This idea was realized as shown in Figure 11. The op-timization preprocessing was made within MSC/PA-TRAN. Using the MSC/CONSTRUCT GUI withinMSC/PATRAN the modifiable design nodes were defi-ned and the optimization control file was generated.

The optimization control file includes e.g. the definitionof the objective function, the constraints as well as op-tional restrictions. Then the nonparametric shape opti-mization with MSC/CONSTRUCT SHAPE wasstarted. This resulted in an optimum shape and a cor-responding displacement vector, which describes thechange from the original shape to the optimum shapeof MSC/CONSTRUCT. With the hipop.v691 DMAP al-ter a modal analysis was run providing eigenformswhich were then considered to be further shape basisvectors. The above mentioned displacement vector

from the MSC/CONSTRUCT SHAPE run and these ei-genform shape vectors were the parameters for theSOL200 optimization which was finally started.

This approach of coupling the easy and efficient mo-deling and optimization using MSC/CONSTRUCTSHAPE with the robust and general shape optimizati-on capabilities of the SOL200 was verified with thecrank shaft model shown in Figure 12.

The left plot in Figure 13 shows the displacements through the shape optimization withMSC/CONSTRUCT SHAPE based on the start model. The objective of this optimizati-on was the reduction of the stress levels of the design nodes and therefore the homo-genization of these stresses. It led to a new shape of the crank shaft which formed theinput model for a MSC/NASTRAN modal analysis for a couple of eigenfrequencies.The corresponding eigenmodes were than considered as further shape basis vectorsfor the following SOL200 shape optimization which included constraints on the eigen-frequencies.

Figure 11: Flow chart of thecoupled MSC/CONSTRUCTSHAPE andSOL200 shapeoptimization.


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Comparing the plots of Figure 13 one may learn that the shape optimization usingMSC/CONSTRUCT SHAPE led to a design which was already very close to the opti-mum design found by the following SOL200 shape optimization. SOL200 then foundonly minor shape changes.

Figure 12: Initial FE Model for the Crank Shaft Shape Optimization (left) and Design Surfaces(right). Courtesy of BMW AG.

Figure 13: Surface Changes through the Preoptimization with MSC/CONSTRUCT SHAPE(left) and through the following SOL200 Optimization (right). Courtesy of BMW AG.


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Besides cutting the preprocessing time from 2 weeks to 5 hours the use of MSC/CON-STRUCT SHAPE led also to a reduction of the computing time for the SOL200 run bya factor of 10. This is due to the fact that running the SOL200 shape optimization basedon a good start design reduces the number of required iterations.

The shape optimization using MSC/CONSTRUCT SHAPE and the SOL200 thereforeshows the following benefits: The generation of shape basis vectors could be performed automatically. This process is fully embedded in MSC/PATRAN and easy-to-use. The combination of this software resulted in tremendous time savings without

losing generality.

6. Conclusion

The work done in the HIPOP (High Performance OPtimization) project resulted insound improvements of the throughputs. With this software the topology and shape op-

timization of large real world models is possible and much more important: efficient.With the performance improvements within MSC/CONSTRUCT the speedups of MSC/NASTRAN can directly be applied to the optimization and therefore result in the samespeedups for the whole optimization. This was shown utilizing Parallel MSC/NASTRAN(PMN) on a distributed memory machine like the IBM-SP2 applying it to a large teststructure from the automotive industry.

Combining MSC/CONSTRUCT SHAPE with the SOL200 allows not only the automa-tion of the shape optimization process but also result in tremendous time savings forthe preprocessing and for the computing.

With the software modules presented in this article the design engineer as well as theanalyst have tools to get clear design decisions throughout the product developmentprocess. The use of MSC/NASTRAN guarantee for the robust and reliable results.

The performance improvements and the functional extensions made in MSC/CON-STRUCT will be available with the next release.

Figure 14: How MSC/CONSTRUCT TOPOLOGY and SHAPE and the SOL200 fit into theproduct development process.


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7. Acknowledgements

This work was supported in part by DG III of the European Commission under the ES-PRIT Contract No. 24462. This support is gratefully acknowledged.

8. References

8.1 Shape Optimization

[1] Raasch, I.; Irrgang, A.: Shape Optimization with MSC/NASTRAN; MSC/NA-STRAN European Users Conference, Rome, 1988

[2] Chargin, M.; Raasch, I.: Structural Optimization with MSC/NASTRAN revisited[3]in Version 66, MSC/NASTRAN European Users Conference, Paris, 1990

[3] Sauter, J.: CAOSS oder die Suche nach der optimalen Bauteilform durch eine ef-

fiziente Gestaltoptimierungsstrategie. XX. Internationaler Finite Elemente Kon-gress, Tagungsband, 18.-19. November 1991, Baden-Baden

[4] Kasper, K.; Sauter, J.; Friedrich, M.: Industrieller Einsatz von Optimalittskrite-rien zur parameterfreien Formoptimierung von Tragwerken. ANSYS-USERS-MEETING, Bamberg, Oktober 1993

[5] Sauter, J.: A New Shape Optimisation Method Modelled on Biological Structures,Benchmark, page 22-26, September 1993

[6] Raasch, I.: Structural Optimization with Solution 2001 in the Design Process;MSC/NASTRAN World Users' Conference, Lake Buena Vista, 1994

[7] Moore, G.J.:MSC/NASTRAN Design Sensitivity and Optimization, Users Guide,Version 68, 1994

8.2 Topology Optimization

[8] Sauter, J.; Mulfinger, F.; Mller, O.: Neue Entwicklungen im Bereich der Ge-stalt- und Topologieoptimierung. ANSYS-USERS-MEETING, Arolsen, Oktober1992

[9] Allinger, P.; Brandel, B.; Mller, O.; Sauter, J.: Optimierung von Bauteilen mitCAOSS und VECFEM/S, ODIN-Abschlusymposium vom 3.-4. Mrz 1994,Karlsruhe

[10] Allinger, P.; Bakhtiary, N.; Friedrich, M.; Mller, O.; Mulfinger, F.; Puchinger,M.; Sauter, J.: A New Approach for Sizing, Shape and Topology Optimization,Paper-No. 960814, SAE Congress, Detroit, February 1996

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